In an amusement park ride called The Roundup, passengers stand inside a 17.0m -d
ID: 1290846 • Letter: I
Question
In an amusement park ride called The Roundup, passengers stand inside a 17.0m -diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure
a) Suppose the ring rotates once every 5.30s . If a rider's mass is 54.0kg , with how much force does the ring push on her at the top of the ride?
b)Suppose the ring rotates once every 5.30s . If a rider's mass is 54.0kg , with how much force does the ring push on her at the bottom of the ride?
c)What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?
In an amusement park ride called The Roundup, passengers stand inside a 17.0m -diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure a) Suppose the ring rotates once every 5.30s . If a rider's mass is 54.0kg , with how much force does the ring push on her at the top of the ride? b)Suppose the ring rotates once every 5.30s . If a rider's mass is 54.0kg , with how much force does the ring push on her at the bottom of the ride? c)What is the longest rotation period of the wheel that will prevent the riders from falling off at the top?Explanation / Answer
The centripetal accelerating force is always towards the centre of the ring.
But the apparent centrifugal force experienced by the passenger is in the opposite direction.
So its a downward force assisting gravity at the bottom of the ride, and upward against gravity at the top.
Tangential velocity v = circumference / rotation period T
When T = 5.3s, v = pi*17m / 5.3s = 10.07 m/s
The apparent centrifugal force is F = m*v^2/r = 54kg * (10.07m/s)^2 / 8.5m = 644.22N
The force of gravity is f = mg = 54kg * 9.81m/s^2 = 529.74N
So at the top of the ride, net force = 644.22N - 529.74N = 114.48N
At the bottom of the ride, net force = 644.22N + 529.74N = 1173.96N
Minimum centrifugal force required = force of gravity = 529.74N
So m*v^2/r = 529.74N
v = 9.13m/s = minimum tangential velocity to prevent 54kg riders falling off at the top
v = pi*d / T
So the maximum rotation period T = pi*17m / 9.13m/s = 5.85 seconds
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